**Area and polygons :**

A polygon is a plane shape with straight sides.The area of a polygon measures the size of the region enclosed by the polygon. It is measured in units squared.

Here you can find area of different polygons.

A triangle with all three sides of equal length. All the angles are 60°. Area of equilateral triangle = (√3/4) a² | |

A scalene triangle is a triangle that has three unequal sides. Area of scalene triangle = √s(s-a)(s-b)(s-c) | |

A parallelogram is a quadrilateral with opposite sides parallel. Area of parallelogram = b x h | |

A shape which is having four sides is generally called quadrilateral. Area of quadrilateral = (1/2) x d x (h₁+h₂) | |

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. Area of rectangle = length x breadth | |

A plane figure with four equal straight sides and four right angles. Area of square = 4 a | |

A rhombus is a parallelogram with four equal sides and opposite equal angles. Area of rhombus = (1/2) x (d₁ x d₂) | |

A quadrilateral with one pair of sides parallel. Area of trapezium = (1/2) x h (a+ b) |

**Example 1 :**

Find the area of the parallelogram

**Solution :**

**Area of the parallelogram = b x h**

here base (b) = 14 cm and

height (h) = 6 cm

= 14 x 6

= 84 cm²

Let us see the next example problem on "Area and polygons"

**Example 2 :**

What is the area of a parallelogram that has a base of 12 ¾ in and a height of 2 ½ in.?

**Solution :**

**Area of the parallelogram = b x h**

here base (b) = 12 ¾ inches => 51/4 inches

height (h) = 2 ½ => 5/2 inches

= (51/4) x (5/2)

= (255/8)

Converting this improper fraction into mixed fraction, we get 31 ⅞ square inches

Let us see the next example problem on "Area and polygons"

**Example 3 :**

Find the area of trapezoid

**Solution :**

**Area of the trapezoid = (1/2) h (a + b)**

**a = 36 inches, b = 42 inches and h = 24 inches**

** = (1/2) x 24 (36 + 42)**

** = (1/2) x 24 x 78**

** = 936 in**²

**Example 4 :**

The bases of a trapezoid are 11 meters and 14 meters. Its height is 10 meters. What is the area of the trapezoid?

**Solution :**

**Area of the trapezoid = (1/2) h (a + b)**

**a = 11 m, b = 14 m and h = 10 m**

** = (1/2) x 10 (11 + 14)**

** = 5 x 25**

** = 125 m**²

**Example 5 :**

The diagonals of a rhombus are 21 m and 32 m. What is the area of the rhombus?

**Solution :**

Area of rhombus = (1/2) x (d₁ x d₂)

d₁ = 21 m and d₂ = 32 m

** = (1/2) x (21 x 32)**

** = 21 x 16**

** = 336 m**²

**Example 6 :**

Find the area of the given figure. Explain how you found your answer.

**Solution :**

In the given figure we can find two shapes trapezium and rectangle.

ABCD is a trapezium

DCEF is a rectangle

Area of the given figure

= area of trapezium + area of rectangle

Area of trapezium (ABCD) = (1/2) x h (a+ b)

DC = EF = 18 ft

a = 10 ft, b = 18ft and h = 6 ft

= (1/2) x 6 x (10 + 18) ==> 84 square ft

Area of rectangle (DCEF) = length x breadth

length = 18 ft and breadth = 12 ft

** = 18 x 12 ==> 216 square ft**

**Area of given figure = 84 + 216 **

**= 300 square ft**** **

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

After having gone through the stuff given above, we hope that the students would have understood "Area and polygons".

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